# Adaptive RBF-KAN: A Comparative Evaluation of Dynamic Shape Parameters in Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2605.21534 · HTML: https://mlsanity.com/paper/2605.21534/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 36 references that are in the map.
- First posted on arXiv 20 May 2026.

## Builds on (most cited first, 13 of 13)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (2024)
- [Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem](https://mlsanity.com/paper/1906.11945/) (2019)
- [Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomials](https://mlsanity.com/paper/2406.02583/) (2024)
- [Kolmogorov-Arnold Fourier Networks](https://mlsanity.com/paper/2502.06018/) (2025)
- [A Practitioner's Guide to Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2510.25781/) (2025)
- [Power-Enhanced Residual Network for Function Approximation and Physics-Informed Inverse Problems](https://mlsanity.com/paper/2310.15690/) (2023)
- [Stable Weight Updating: A Key to Reliable PDE Solutions Using Deep Learning](https://mlsanity.com/paper/2407.07375/) (2024)
- [Granger Causality Detection with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2412.15373/) (2024)

## Abstract (arXiv)

Kolmogorov-Arnold Networks (KANs) approximate multivariate functions using learnable univariate edge functions, typically parameterized by B-spline bases. Although effective, spline-based implementations can be computationally expensive. A modified version of KANs, called FastKAN, improves efficiency by replacing splines with Gaussian radial basis functions (RBFs), but it relies on a fixed kernel and shape parameter. In this work, we extend the RBF-based KAN framework by introducing a broader family of radial basis kernels and by initializing the kernel shape parameter using leave-one-out cross-validation (LOOCV). To the best of our knowledge, this is the first study that integrates LOOCV-based kernel scale estimation with deep KAN training. We also introduce Mat'ern and Wendland kernels into the KAN framework for the first time, enabling more flexible basis representations beyond the Gaussian kernel used in FastKAN. The LOOCV estimate provides a data-driven initialization of the kernel scale, which is subsequently refined during network training. The proposed adaptive RBF-KAN is evaluated on several two-dimensional benchmark functions. The results highlight the importance of kernel selection and adaptive shape parameters, with different kernels showing advantages for smooth functions, discontinuities, and oscillatory patterns. Overall, combining LOOCV-based initialization with adaptive kernel learning provides a practical strategy for improving RBF-based KAN models.